The research work proposed herein is: (1) To obtain numerical solutions of momentum and diffusion transport equations for the case of blood flowing through a semipermeable conduit, and (2) To verify the numerical solution with the experimental data of Dr. Stewart (Appendix A) and of Mr. Kofler and Mr. Tatarchuk (Appendix D). This is the first step in our final goal of designing efficient, economical and reliable blood oxygenation and hemodialysis units. It is estimated that it will take 1 year to accomplish the proposed work.